ACTUARIES & DATA SCIENCE

Jerome Tuttle, FCAS, CPCU

Retired Actuary

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What is an actuary?

• The mathematicians of the insurance industry.
• A business professional who deals with the financial impact of risk and uncertainty.
• Analyzes, manages, and measures the financial impact of risk and uncertainty.
• Develops and validates models and communicates results to guide decision-making.
• Actuaries in movies:

Jack Nicholson – Ben Stiller –

About Schmidt (2002) Along Came Polly (2004)

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Insurance is a unique business

• We don’t know our cost (claims) when we sell the policy, and with some claims we don’t know for many years.
• We are not required to sell to everyone – similar to bank loans and college admissions.
• We do not charge the same price to everyone. This is REQUIRED by law, e.g., FL Statute 627.062:

■ Rates may not be unfairly discriminatory.

■ A rate is unfairly discriminatory to a group of risks if the rate does not bear a reasonable relationship to the expected loss experience among the risks.

$$$$$ $$$

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The intersection among math/stats, computer sci, & subject matter knowledge to extract meaningful insights from data translating into tangible business value.

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What is data science?

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Examples of data science e

• Internet search engine algorithms.
• Targeted advertising and recommendations.
• Target Stores sent diaper coupons to the pregnant teenager before she told her father. (Folklore?)
• Moneyball and sports analytics.
• Better singles matching on dating websites.
• Disease diagnosis, personalized healthcare recs.
• Data driven crime prediction, facial recognition, terrorist forecasts.
• Which tweets did Trump write, and which did his staff write?

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Actuaries and data science

• “Actuaries were among the first data scientists.” (Colin Priest, actuary turned data scientist at Data Robot, Singapore.)
• Actuaries are strongest at math/stat and domain knowledge (we study insurance, besides math/stat).
• Data scientists are strongest at computer science, especially coding, data manipulation and joining tables, theory of machine learning (training versus testing, overtraining), and machine learning algorithms.
• Actuarial exams now include:

Generalized linear models, K-nearest neighbors, K-means clustering, Bayes classifier, decision trees, random forest, principal component analysis. Also a predictive anal specialty.

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Randomly split data into training versus testing data

RMSE on test data = √[∑ (Actual – Predicted)² / n]

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Some actuarial examples of data science techniques

• If predictive modeling refers to estimating insurance costs, then actuaries have been doing this forever.
• Today predictive modeling is computationally intensive, often testing all possible permutations of variables, transformations, etc
• The 2 broad categories in data science are prediction and classification. Classification is predicting a category.
• Prediction often involves types of regression. Linear regression is being replaced by more flexible Generalized Linear Models.
• Classification includes:

Decision trees: underwriting

Clustering: territories

Principal component analysis: detect fraud

• In the following examples, assume n independent variables and p data values.

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For insurance rating, we group (hopefully) similar customers into classes and charge an average rate for the class. Classification is rarely perfect.

Before classification After classification

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Insurance classes may include age, gender, urban / rural territory, marital status, miles driven, claims history, car type, car age, etc.

But within each n-dimensional slice, there is still considerable variability. A company wants to choose the better than average customers within each class to make a profit.

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Generalized Linear Models: pricing

• Traditionally we used classical linear regression, and we treated our pricing by class as multiplicative:
• Base rate = $100

Times factor for Age i = 1.50

Times factor for Gender j = 1.20

Times factor for Territory k = 1.40, ... , etc.

• This disregards interactions between classes and makes assumptions on normality and common variances.
• GLMs consist of wider range of models with response variable assumed to be a member of exponential family.
• Results in some factors being reduced, others increased.
• Other applications of GLM:

Effect of telematics on claims

Underwriting score cards

Predict claims likely to settle far above their initial estimate

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Decision trees: underwriting

• Sequentially splits data into categories having similar values for dependent variables.
• Uses statistic such as Gini Index to do split.
• Possible variables: no. years renewed, occupation, premium payment history, telematics (speed, braking, time of day, etc.)

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Clustering: territories

• Partitions data into classes based on how closely data is grouped. Iteratively updates centers and re-partitions.
• There is no dependent variable.
• Another use is clustering similar occupations.
• Florida has 28 rating territories in auto.

Yao, J. (2008). Clustering in ratemaking; applications in territories clustering. Casualty Actuarial Society Predictive Modeling Seminar

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Principal component analysis: fraud detection

• Reduces a large no. of variables to a smaller no.

of mutually uncorrelated variables that preserves

as much variability as possible.

• Auto fraud (staged accident, inflated bills, collusive medical or body shops) hard to detect by first-level claim examiners.
• No dependent variable. Data doesn’t say which claim is definitely fraud. Much fraud is undetected.
• Data often ordinal, e.g. suspicion level = {1, 2, …, 5} for each variable (# chiropractor visits, hi vol med provider).
• Goal is overall fraud suspicion score, iteratively weighting indiv variables based on their consistency and correlation to overall score.
• Why do we study Linear Algebra? PCA uses orthogonal transformations, eigenvectors.

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Credit scoring

• A numerical score of a person’s creditworthiness. Ideally correlates with claims experience and provides additional predictive ability beyond traditional rating variables.
• Permitted by FL Statute 626.9741.
• Criticized as unfair to minorities and low-income people, although analysts dispute the criticism.
• Variables include debt/asset ratio, late payment history…
• Data science techniques: clusters, trees, GLM, PCA, …

■ Loss ratio = f (variables X1, …, Xn)

• Often used in the decision whether or not to offer insurance, but not used to determine the price.
• Many publicly available credit risk databases for credit cards and loans, e.g., Kaggle competition at Kaggle.com/c/GiveMeSomeCredit/

■ Probability of default = f (variables X1, …, Xn)

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Text Analysis

• Most data is numerical and is neatly captured in fields
• Free-form text is a potential gold mine of information, but it requires effort to extract gold nuggets.
• Misspellings, synonyms, stems like “ing” and “ed”, etc.
• Look for freq. words, groups of words appearing together.
• What kinds of claims are occurring? “Water” may be a captured field, but “water & basement” or “water & ceiling” may be more helpful in finding trends.
• What words signal potential large claim amount?
• How do people feel about insurance ads? Identify sentiments in customer surveys & tweets.
• FL Statute 627.4145 requires insurance policies have min 45 score on Flesch readability test.

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References

• Frees, E. W., et. al. (2016). Predictive modeling applications in actuarial science. New York: Cambridge University Press.
• Healy, K. (2018). Data visualization. Princeton, NJ.: Princeton University Press.
• James, G., et. al. (2017). An introduction to statistical learning with applications in R. New York: Springer
• Zhao, Y. (2013). R and data mining. San Diego: Academic Press.

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